Number of subsets of {1..n} with all distinct lengths of maximal runs (increasing by 1).

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =13a(5) =24a(6) =44a(7) =77a(8) =135a(9) =236a(10) =412a(11) =713a(12) =1215a(13) =2048a(14) =3434a(15) =5739a(16) =9559a(17) =15850a(18) =26086a(19) =42605a(20) =69133a(21) =111634a(22) =179602a(23) =288069a(24) =460553a(25) =733370a(26) =1162356a(27) =1833371a(28) =2878621a(29) =4501856